From TFL’s weekly weekend travel email:
This leaves us with only 2 trains an hour on Saturday and 4 trains an hour on Sunday:
Saturday
Forest Hill to London Bridge at 0643 and 0713 then at 14 and 44 past each hour from 0744 to 2314
London Bridge to Forest Hill at 10 and 40 past each hour from 0610 to 2340 then 0020 & 0035
Sunday
Forest Hill to London Bridge at 0749 and 0805 then at 01, 18, 31 and 48 past each hour from 0818 until 1231 then at 01, 16, 31 and 46 past each hour from 1246 until 2316 then 2346
London Bridge to Forest Hill at 0731, 0738 and 0801 then at 08, 24, 38 and 54 past each hour from 0808 to 2254 then 2331 and 2350
Southbound services from Forest Hill on Saturday terminate at Coulsdon Town but on Sunday terminate at Caterham/Tattenham Corner or Crystal Palace
The weekend shutdowns on London Overground are currently due to continue until the bank weekend of 29/30/31 August.